Heat bacon drippings in a skillet over medium heat; whisk flour into drippings until smooth. Reduce heat to low and cook the flour mixture until it turns a caramel brown color, stirring constantly, about 15 minutes. Be careful, the roux burns easily. Stir in salt and black pepper.
Whisk 1/2 cup milk into the roux until thoroughly blended. Continue whisking milk into the gravy, 1/2 cup at a time, whisking in each amount of milk completely before adding more. Bring gravy to a simmer and whisk constantly until thick, smooth, and bubbling.